NAME

Math::PlanePath::MathImageSierpinskiCurve -- Sierpinski octant curve

SYNOPSIS

use Math::PlanePath::MathImageSierpinskiCurve;
my $path = Math::PlanePath::MathImageSierpinskiCurve->new;
my ($x, $y) = $path->n_to_xy (123);

DESCRIPTION

This path is an integer version of the self-similar curve by Sierpinski going along the X axis and making triangular excursions.

                                          63-64            14
                                           |  |
                                          62 65            13
                                         /     \
                                    60-61       66-67      12
                                     |              |
                                    59-58       69-68      11
                                         \     /
                              51-52       57 70            10
                               |  |        |  |
                              50 53       56 71       ...   9
                             /     \     /     \     /
                        48-49       54-55       72-73       8
                         |
                        47-46       41-40                   7
                             \     /     \
                  15-16       45 42       39                6
                   |  |        |  |        |
                  14 17       44-43       38                5
                 /     \                 /
            12-13       18-19       36-37                   4
             |              |        |
            11-10       21-20       35-34                   3
                 \     /                 \
       3--4        9 22       27-28       33                2
       |  |        |  |        |  |        |
       2  5        8 23       26 29       32                1
     /     \     /     \     /     \     /
 0--1        6--7       24-25       30-31                 Y=0

 ^
X=0 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 ...

FUNCTIONS

$path = Math::PlanePath::MathImageSierpinskiCurve->new ()

Create and return a new path object.

($x,$y) = $path->n_to_xy ($n)

Return the X,Y coordinates of point number $n on the path. Points begin at 0 and if $n < 0 then the return is an empty list.

Fractional positions give an X,Y position along a straight line between the integer positions.

$n = $path->n_start()

Return 0, the first N in the path.

SEE ALSO

Math::PlanePath, Math::PlanePath::KochCurve